When searching a contact to share a folder with, the first name, surname and even the email address should be listed as results if they contain the string you are looking for.

Today search "Smith" to find "John Smith" doesn't give any result, but searching "John" will give "John Smith". The issue is that something you only know the first name or last name of the contact you're looking for. Mickey Mouse might be registered as "Mouse Mickey" and won't be found searching "Mickey". Disturbing.